UV radiation isn't visible to the human eye, so how come we can see it as a purple/violet light from a UV lamp? Is it just because the lamps aren't perfect and end up emitting some light at a higher frequency? Or do they add some purple light intentionally? Or is there some more complex mechanism going on?
There are several kinds of "UV Light." Only kind I know of that "looks purple" is a so-called black light.
Black lights emit UV that is very close to the top-end of the visible spectrum. The designers try to minimize the visible radiation so that it won't wash out the light emitted by fluorescent substances in the field, but it's hard to filter all of the visible out.
The visible tail looks "purple" because the "red" receptors in your eye have some sensitivity at the shortest visible wavelengths. The visible leakage from a black light stimulates both "red" and "blue" receptors in your eye, and you perceive purple.
Other types of UV lamp (e.g., germicidal lamps) generally put out a lot of visible light that they don't bother to filter out because (A) it does not interfere with the application (e.g., visible light won't stop the UV from killing the germs) and (B) for safety reasons (i.e., so you know when you're looking at the light, which you shouldn't because it's dangerous.)